The use of a lightweight antenna system is a desirable goal for space based communication systems. A system that uses a lightweight polymeric material configured as a large sheet that may be greater than thirty meters in diameter has been proposed as a suitable candidate for such applications. There exists, however a need to shape and maintain the sheet as to reflect directed signals in order to act as an antenna. Prior determinations of membrane shape have been the use of interferometry where diffraction pattern returns are analyzed. Diffraction shape determinations have been applied to adaptable mirrors and rigid reflective structures. Some designs for shape determination have used sensors that are attached to the antenna surface. However, the use of sensors adds weight to the membrane and thus detracts from the proposed lightweight property of the design.
U.S. Pat. No. 6,709,116, issued to Raskar, on Mar. 23, 2004 entitled a shape-adaptive projector system teaches a method to adapt an output image to a shape of a display surface. First, a structured pattern is projected onto the display surface by a projector. An image having a structured pattern is acquired by a camera in a fixed physical relationship with the projector. From the input image, a mesh of the structured pattern is determined in a coordinate frame of the projector. Coordinates of a texture are determined in the coordinate frame of the projector. The coordinates of the texture are updated according to the display region. The texture is then mapped to the mesh, and the textured mesh is rendered on the display surface. Patterned illumination of an object and the capturing of returns by a camera are well known.
U.S. Pat. No. 6,664,956, issued to Erdem on Dec. 16, 2003, entitled method for generating a personalized 3-D face model, teaches a method for generating a 3-D model of a person's face is disclosed. The 3-D face model carries both the geometry shape and the texture color characteristics of the person's face. The shape of the face model is represented via a 3-D triangular mesh, while the texture of the face model is represented via a 2-D composite textured image. The triangular geometry mesh is obtained by deforming a predefined standard 3-D triangular mesh based on the dimensions and relative positions of the person's facial features, such as eyes, nose, ears, lips, and chin. The texture image is obtained using a set of 2-D images of the person's face, which are taken from particular directions such as front, right, left, etc, and modifying the images along region boundaries to achieve seamless stitching of color on the 3-D face model. The directional images are taken while the mouth is closed and the eyes are open. In order to capture the color information of the facial regions that are not visible in the directional images, that is, the inside of the mouth and the outside of the eyelids, additional 2-D images are also taken and included in the textured image.
U.S. Pat. No. 6,760,488, issued to Moura on Jul. 6, 2004, entitled system and method for generating a three-dimensional model from a two-dimensional image sequence, teaches a system for generating a three-dimensional model of an object from a two-dimensional image sequence. According to one embodiment, the system includes an image sensor for capturing a sequence of two-dimensional images of a scene. The scene includes the object. The system also includes a two-dimensional motion filter module in communication with the image sensor for determining from the sequence of images a plurality of two-dimensional motion parameters for the object. The system further includes a three-dimensional structure recovery module in communication with the two-dimensional motion filter module for estimating a set of three-dimensional shape parameters and a set of three-dimensional motion parameters from the set of two-dimensional motion parameters using a rank one factorization of a matrix.
U.S. Pat. No. 6,756,590, issued to Kazui on Jun. 29, 2004, entitled Shape measurement method and apparatus, teaches an electron beam applied from an electron gun. The beam is reflected off a surface of a specimen placed on a stage that is tilted at a tilt angle. Return intensities are measured by an electron detector. Based upon the measurement, an image processing unit calculates a slope angle of the surface of the specimen, and determines candidates for cross-sectional shape of the specimen. Signal intensity of the electromagnetic wave is reflected from a surface having a cross-sectional shape of each of the candidates when the tilt angle is estimated, and then compared with a signal intensity actually measured by the electron detector with the tilt angle. Consequently, cross sectional shape and three-dimensional shape can be determined based upon a result of comparison, without utilizing a matching process of feature points.
U.S. Pat. No. 6,611,343 issued to Frankowski on Aug. 26, 2003, entitled method and device for 3D measurement teaches a procedure and a device for contact-free, optoelectronic 3D measuring of objects. Especially partially automated and automated manufacturing processes with constantly decreasing cycle times and higher precision requirements demand modern measuring procedures and devices, monitoring the quality criteria required, and controlling manufacturing processes. A procedure and device is introduced to extend the application of computerized 3D-measuring technology and for online-integration into the production process. Within a single recording cycle, arbitrary line patterns suitable for 3D-measuring technology and defined intensity structures are projected via a micromirror projector for object coding.
Hilbert transforms for transforming image data into a complex image is well known using forward transformations, bandpass filtering, and inverse transformations. Two-dimensional phase unwrapping by interpolation is also well known as a key algorithm for topographic mapping with interferometric synthetic aperture radar. A least squares formulation for unwrapping leads to a discrete Poisson equation with boundary conditions to be solved. A large linear system of equations for the unwrapped phase disadvantageously results. For example a 100 by 100 sample data set leads to a sparse matrix with 10,000 rows and 10,000 columns to invert. 2-D unwrapped phase data has been generated from complex images. 2-D unwrapped phase data has been interpolated to a coordinate system. The generation of unwrapped phase data and the unwrapping of phase data are well known.
The prior shape determination methods have used various means and processes, such as diffraction methods, for determining the shape of a surface. Various processing means have been used to implement Hilbert transforms of image data, unwrapping of wrapped phase data, and interpolations of wrapped data to a coordinate system. Such processes have not been integrated for adaptively correcting deformities in a flexible membrane. These and other disadvantages are solved or reduced using the invention.